In this paper we analyze the reliability of a simple broadcasting scheme for hypercubes (HCCAST) with random faults. We prove that HCCAST (n) (HCCAST for the n-dimensional hypercube) can tolerate Θ(2n/n) random faulty nodes with a very high probability although it can tolerate only n - 1 faulty nodes in the worst case. By showing that most of the f-fault configurations of the n dimensional hypercube cannot make HCCAST (n) fail unless f is too large, we illustrate that hypercubes are inherently strong enough for tolerating random faults. For a realistic n, the reliability of HCCAST (n) is much better than that of the broadcasting algorithm described in [6] although the latter can asymptotically tolerate faulty links of a constant fraction of all the links. Finally, we compare the fault-tolerant performance of the two broadcasting schemes for n = 15, 16, 17, 18, 19, 20, and we find that for those practical valuse, HCCAST (n) is very reliable.

We study all-to-all broadcasting in hypercubes with randomly distributed Byzantine faults. We construct an efficient broadcasting scheme BC1-n-cube running on the n-dimensional hypercube (n-cube for short) in 2n rounds, where for communication by each node of the n-cube, only one of its links is used in each round. The scheme BC1-n-cube can tolerate (n-1)/2 Byzantine faults of nodes and/or links in the worst case. If there are exactly f Byzantine faulty nodes randomly distributed in the n-cabe, BC1-n-cube succeeds with a probability higher than 1(64nf/2n) n/2. In other words, if 1/(64nk) of all the nodes(i.e., 2n/(64nk) nodes) fail in Byzantine manner randomly in the n-cube, then the scheme succeeds with a probability higher than 1kn/2. We also consider the case where all nodes are faultless but links may fail randomly in the n-cube. Broadcasting by BC1-n-cube is successful with a probability hig her than 1kn/2 provided that not more than 1/(64(n1)k) of all the links in the n-cube fail in Byzantine manner randomly. For the case where only links may fail, we give another broadcasting scheme BC2-n-cube which runs in 2n2 rounds. Broadcasting by BC2-n-cube is successful with a high probability if the number of Byzantine faulty links randomly distributed in the n-cube is not more than a constant fraction of the total number of links. That is, it succeeds with a probability higher than 1nkn/2 if 1/(48k) of all the links in the n-cube fail randomly in Byzantine manner.